The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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A strain of bacterial cells doubles inpopulation every 2 days. A single cell is placed in a dish with sufficient nutrients to sustain a colony. Which equation will
calculate d, the number of days after which there will be 256 bacterial cells in
the dish?
The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
How to determine the equation of the number of days?The given parameters are:
Rate, r = doubles every two days
Initial number of strain, a = 1
This means that the function is an exponential function.
An exponential function is represented as:
A(d) = a * r^d
Since the strain doubles every two days, we have:
A(d) = a * r^(d/2)
Substitute the known values in the above equation
A(d) = 1 * 2^(d/2)
Evaluate the product
A(d) = 2^(d/2)
When there are 256 bacterial cells, the equation becomes
2^(d/2) = 256
Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
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The area of the entire figure below is 111 square unit.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
What is the area of the striped rectangle?
The striped rectangle has a total area of 69,375 cm².
How to calculate the area of the striped rectangle?To find the area of the striped rectangle we must carry out the following procedures.
Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.
111cm² ÷ 24 = 4.625cm²According to the above, we infer that each square has an area of 4.625cm².
On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.
3 × 5 = 15Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.
15 × 4.625cm² = 69.375cm²
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PLEASE HELP YOU WILL GET ALOT OF POINTS The triangle on the left is rotated to create the triangle on the right as its
image. Which set of congruence statements below is true?
Answer:
The third one
Step-by-step explanation:
It cannot be the first 2 as the corners wouldn't line up. It cannot be the last one as B and R are not the same angles
The volume of a rectangular box is 3x(3x + 4)(3x - 1). (Drawing is not to
scale.)
Length 3x + 4
Width 3x
Height 3x - 1
Which statement about the volume of the box is tru?
The volume of the rectangular box is the product of the base area and the height 3x - 1
How to determine the true statement?The given parameters are:
Length = 3x + 4
Width = 3x
Height = 3x - 1
The base area of the rectangular box is calculated as
Base area = Length * Width
Substitute the known values in the above equation
Base area = 3x(3x + 4)
This means that the volume of the rectangular box is the product of the base area and the height 3x - 1
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cd+(-6c)=150 when d=4
Answer:
c = -75
Step-by-step explanation:
cd + (-6c) = 150
d = 4
c(4) + (-6c) = 150
4c - 6c = 150
-2c = 150
c = -75
Determine the point (x,y) ( x , y ) on the unit circle associated with the following real number s. Write the exact answer as an ordered pair. Do not round. s=−11π6
The required coordinates of the unit circle for s = -11π/6 is (√3/2, 1/2). Using trigonometric functions, the required answer is calculated.
What are the trigonometric functions?There are six trigonometric functions.
They are sin θ, cos θ, tan θ, sec θ, cosec θ, and cot θ.
Where θ - 0 to 360° or 0 to 2π
Calculation:For a unit circle, the coordinates are given in the form of trigonometric functions as below:
x = cos θ and y = sin θ
Here it is given that s = θ = -11π/6
So, on substituting,
x = cos θ = cos (-11π/6)
⇒ x = √3/2
y = sin θ = sin (-11π/6)
⇒ y = 1/2
Thus, the required coordinate pair is (√3/2, 1/2).
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On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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The functions fand g are defined as follows. f(x) = 3x-1 g(x)=3x³ +5 Find f(-6) and g (-4). Simplify your answers as much as possible. ƒ(-6) = g (-4) =
Answer:
f(-6)= -19 and g(-4)= -187
Please help!!!!!!!!!!!!!!!!
Answer: Option (3)
Step-by-step explanation:
[tex]\frac{1}{6a^2}-\frac{5b}{3a^3}+\frac{b^2}{4a}\\\\=\frac{2a}{12a^3}-\frac{20b}{12a^3}+\frac{3a^2 b^2}{12a^3}\\\\=\frac{3a^2 +b2 +2a-20b}{12a^3}[/tex]
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Because the parabola intercepts the x-axis only once, we conclude that the discriminant is 0.
What can we say about the discriminant?
For a quadratic equation:
y = a*x^2 + b*x + c
The discriminant is:
D = b^2 - 4ac
If D = 0, there is only one real zero.If D > 0, there are two real zeros.If D < 0, there are two complex zeros.In the graph we can see that the parabola intercepts the x-axis in its vertex, then the parabola has only one real zero, then we conclude that the discriminant is equal to zero.
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Show Work Please Thank You
Answer:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
Step-by-step explanation:
We are given the trigonometric equation of:
[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]
Let u = 4x then:
[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]
Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).
[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Convert u-term back to 4x:
[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Divide both sides by 4:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.
Therefore:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
A sundae requires 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries. Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries. Let S denote the number of sundaes he makes and M the number of milkshakes he makes. Write an inequality that represents the condition based on the number of ice-cream scoops. Write an inequality that represents the condition based on the number of strawberries.
The system of inequalities be
3x+2y ≤ 25, 4x+6y ≤ 37
1) Maximum number of sundaes possible exists 9.
2) Maximum number of milkshakes possible exists 6.
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
What is system of inequalities?A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.
Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x represent the number of sundaes he creates and y the number of milkshakes he creates.
We represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
System of inequalities:
Sundaes and milkshakes with at most 25 ice-cream scoops exist
33x+2y ≤ 25.
Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.
1) Maximum number of sundaes possible:
Maximum number of sundaes possible when y = 0
From the graph y = 0 at x = 9.25
Therefore, the maximum number of sundaes possible exists at 9.
2) Maximum number of milkshakes possible:
Maximum number of milkshakes possible when x = 0
From the graph x = 0 at y = 6.167
Therefore, the maximum number of milkshakes possible exists at 6.
3) Combination that utilizes the most of both Ice-cream and Strawberries:
A combination of both is possible there exists an intersection of both the equation.
From the graph, the intersection point exists x = 7.6 and y = 1.1.
Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
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MY NOTES
lim
n18
ASK YOUR TEACHER
Use the Limit Comparison Test to determine the convergence or divergence of the series.
00
n=1
n3
converges
O diverges
n+ 3
n+ 3
n3-5n+8
- 5n+ 8
Need Help?
-
=L>0
Read It
9,433
PRACTICE ANOTHER
Watch It
AUG
3
tv♫♬
(a
A
Part 1) [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.
Part 2) The series converges
======================================================
Work Shown:
[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]
[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]
Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]
either converge together or diverge together due to the Limit Comparison Test.
But the simpler series is known to converge (p-series test).
Therefore, the original series converges as well.
The two series likely don't converge to the same value, but they both converge nonetheless.
The accompanying data are the caloric contents and the sugar contents (in grams) of 11 high-fiber breakfast cereals. Find the equation of the regression line. Then construct a
scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not
meaningful to predict the value of y, explain why not.
(a) x = 160 cal
(b)x= 90 cal
(c)x= 175 cal
(d)x=198 cal
Click the icon to view the table of caloric and sugar contents.
The regression equation based on the information given about the sugar contents will be 0.18x - 20.84.
How to explain the regression?It should be noted that from the information, the accompanying data are the caloric contents and the sugar contents of 11 high-fiber breakfast cereals.
The sugar content will be:
a. 160 calories
= 0.18x - 20.84.
= 0.18(160) - 20.84
= 7.96
b. 90 calories
= 0.18x - 20.84.
= 0.18(90) - 20.84
= -4.64
c. 175 calories
= 0.18x - 20.84.
= 0.18(175) - 20.84
= 10.66
d. 208 calories
= 0.18x - 20.84.
= 0.18(208) - 20.84
= 16.6
Therefore, the sugar contents is illustrated above.
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Write your answers as fractions in the format 1/2.
If a learner is picked at random, what is the probability that they are
female and use public transport?
The learner rejoins their class mates and another learner is picked at
random. What is the probability that they are female and walk/cycle to
college?
The probability that they are female and use public transport is [tex]\mathbf{=\dfrac{1}{3}}[/tex]
The probability that they are female and walk/cycle to college is [tex]\mathbf{=\dfrac{1}{9}}[/tex]
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is too probable to occur or how probable a statement is to be true.
Probability is synonymous with possibility. It is a mathematical field that is concerned with the occurrence of a random event. The value ranges from zero to one. The definition of probability is to predict the degree to which something is likely to occur. To determine the likelihood of a particular event occurring, we must first determine the total number of possible outcomes.
Mathematically:
[tex]\mathbf{Probability = \dfrac{number \ of \ required \ outcomes}{total \ number \ of \ possible \ outcomes}}[/tex]
From the table in the image attached below.
The probability that they are female and use public transport is:
[tex]\mathbf{=\dfrac{9}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{3}}[/tex]
Also, the probability that they are female and walk/cycle to college is:
[tex]\mathbf{=\dfrac{3}{27}}[/tex]
[tex]\mathbf{=\dfrac{1}{9}}[/tex]
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Solve the system of equations below using a matrix equation.
2x + y = - 7
x − y = 4
Select one:
a.
( 1, 5 )
b.
( - 1, - 5 )
c.
( - 1, -2 )
d.
( 0, - 7 )
Answer is b. ( -1, -5)
Answer is b. (-1, -5)
Step by step
Substitute the x and y values into both equations to find equality
Answer b. Makes both equations equal
2x + y = -7
2(-1) + (-5) = -7
-2 -5 = -7
-7 = -7
it equals now let’s do the 2nd one
x - y = 4
-1 -(-5) = 4
4 = 4
This one equals too. I did the math on the other three answers and they did not equal.
a number line shows the whole numbers from 0 to 10 describe where you would plot square root 30
Which of the following is equivalent to (5)7/3
Answer:
11 and 2/3
Step-by-step explanation:
The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.
What is exponential form?The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.
Given: [tex]$(5)^{7/3[/tex]
The given expression contains an exponent of (7/3)
When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.
The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]
Therefore, the correct answer is ³√5⁷.
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you are considering an investment into Company XYZ and need to determine the company's value and the appropriate investment amount. You have been provided with historical financial statements for the past three years in order to build a forecast model. Key assumptions to use include:
Future sales revenue is assumed to increase at 2.5% annually.
Gross margin for 2021E is assumed to be equal to the average gross margin % for 2019 and 2020, but will decrease by 2.5% (i.e. 250 bps) each year thereafter
SG&A expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
Depreciation expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
The tax rate for the forecast period is assumed to be equal to the effective tax rate for 2018
Capital expenditures for any given year in the forecast period is assumed to be 3x the prior year's depreciation expense. For example, 2021 capital expenditures is equal to 3x 2020 depreciation expense.
No new debt or equity is assumed to be issued
Download CFI_-_FMVA_Practice_Exam_Case_Study_A.xlsx and answer the following 12 questions.
1
What is Gross Profit in 2028E using the assumptions listed above and on the Control Panel?
$17,545
$30,704
$27,780
$40,938
Option A is correct. The gross profit that has been calculated for this year is given as 17545
How to solve for the gross profit22050 × 97.5%(100-2.5%) = 21498.75
= 21498.75 × 0.975 = 20961.28
= 20961.28 x 0.975 = 20437.24
= 20437.24 x 0.975 = 19926.31
= 19926.31 × 0.975 = 19428.15
= 19428.15 x 0.975 = 18942.45
= 18942.45 x 0.975 = 18468.80
= 18468.89 × 0.975 = 18017
= 18007 × 0.975 = $17545
Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545
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Solve rs + t = u for the variable s
Answer:
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
Step-by-step explanation:
You have to move the variables (r and t) with u to isolate s.
[tex]rs+t=u[/tex]
[tex]-t[/tex] [tex]-t[/tex]
------------------------
[tex]rs=u-t[/tex]
÷ [tex]r[/tex] ÷ [tex]r[/tex]
------------------------
[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]
HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:
A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
B) ONLY ODD DIGITS CAN BE USED?
C) THE FIRST 3 DIGITS ARE 277?
Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:
a) 900,000.
b) 78,125.
c) 10,000.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:
[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]
Hence the number is:
N = 9 x 10^5 = 900,000.
For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]
Hence the number is:
N = 5^7 = 78,125.
For item c, if the first 3 digits are 277, the parameters are:
[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]
Hence the number is:
N = 10^4 = 10,000.
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When a disease is rare in the general population, doctors are not likely to test everyone. Instead, they only test people that have specific risk factors or show symptoms of the disease. Even if resources are available, why do you think doctors would avoid giving a test for a rare disease to everyone in the general population? Explain using ideas from probability that were explored in this project
(-4) (-2) +2 (6+5) if anyone knows pls tell due dates tomm for homework
Thanks,
Unknownaz05
Answer:
21
Step-by-step explanation:
(-4)(-2)+2(6+5)
(8)+2(11)
10+11
21
Hope this helps! :)
Answer:32
Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32
The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Let y represent the total company fund and x represent the number of staffs.
From the first statement:
y - 50x = -5 (1)
Also:
y - 45x = 95 (2)
From equation 1 and 2:
x = 20, y = 995
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
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Elliot borrows $3,000 from a bank that is charging three percent simple interest per year. If he pays the loan back in six months, how much interest will he pay? $30.00
$45.00
$90.00
$300.00
Answer:
The answer to that question depends
beacuse where ever you are it changes like uk you can pay 100€
or japan it can be around 1000¥
Scenario 2
You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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a studio has 1600 square feet of floor space. the studio then buys the neighboring building and expands by 75%
Answer:
the total new area is 2800 ft²
Step-by-step explanation:
original area: 1600 ft²
new expanded area: 1600 ft² + 75% of 1600 ft²
new expanded area = 1600 ft² + 0.75 × 1600 ft²
new expanded area = 1600 ft² + 1200 ft²
total new area = 2800 ft²
graphs of exponential functions
An example of an exponential graph function has been attached and its' properties are as below.
How to draw the graph of an exponential function?The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.
The reasons for the restrictions are because;
If a ≤ 0, then when you raise it to a rational power, you may not get a real number.
The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.
The graph passes through the point (0,1)The domain is all real numbersThe range is y>0.The graph is increasingThe graph is asymptotic to the x-axis as x approaches negative infinityThe graph increases without bound as x approaches positive infinityThe graph is continuousThe graph is smoothRead more about Exponential Function Graphs at; https://brainly.com/question/2456547
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Find the length indicated
Show work
Answer: 5 units
Step-by-step explanation:
x+2+2x-7=13
solve for x
3x=18
x=6
∴SR: 2x-7
=2(6)-7
=12-7
=5
Answer:
SR = 5
Step-by-step explanation:
[tex]TR=x+2+2x-7=3x-5[/tex]
[tex]3x-5=13[/tex]
[tex]3x=13+5[/tex]
[tex]x=18/3=6[/tex]
[tex]SR=2x-7=2(6)-7=12-7=5[/tex]
Hope this helps
what is the equation of the parabola passing through the points
(0,6). (3, 15.6), and (10,-4)?
Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6